To use a mathematical formula - there is one from queuing theory to calculate the average queue length - you need to make assumptions about the rates at which each node send packets, and the time to service them. The formula work for well known distributions - Poisson, Bernoulli or fixed rate, but real sources rarely follow such models.

Dear Bekan Kitawm,

I do not know the details of her problem. But I think the Little's Formula for queue Type M / M / 1 can be used here.

See for example:

http://perfeval.epfl.ch/printMe/queuingPost.pdf

(See here page 8)

http://staff.um.edu.mt/jskl1/simweb/mm1.htm

http://williams.comp.ncat.edu/comp755/q.pdf

Best regards

Anatol Badach

Cruz Izu Thanks for your explanations! I'm working on Ad-hoc networks esp. on routing protocol. Do you think that mathematical formula would works in this scenario??

In my humble opinion, you cannot.

The mathematical models, that I know, work with a couple of queues, but in an ad-hoc network, the complexity of the model is too high and, usually, they don't work. You have multiples nodes that can change of position in any moment, and the routing protocols can modify the path in any moment, changing the distribution of traffic and with this, the queues.

Usually, with the actual bit rates in the transmission (with 11n a common bit rate is 150Mb/s), the mean size of the queues is from 0 to 2 packets (I have measured the mean queue using a simulator). The physical medium can unload the queues really quickly, the problem with the queues is not the mean value, that is the value that you can obtain with a very complex mathematical model (due to the connection between queues and node), the problem is some instantaneous values, when you can cause overflow the queues, and I don’t know any mathematical model that computes this instantaneous value.

Anatol Badach Thanks for your helps and quick references! I'm working on Ad-hoc networks esp. on routing protocol. Do you think those mathematical formula would works in this scenario?? Am getting very tired with. Please kindly help me if you knows!

Alfonso Ariza Quintana Thanks! It was my research idea which am fighting with for so long. So do you think that I've to start another idea from scratch skipping this? Am M.Sc student

If you are asking, if it is possible to develop some model for your thesis

yes

https://pdfs.semanticscholar.org/b258/19ecf88c19457e3833550e0c0901aa504110.pdf

(The results in the article doesn't show that is practical for a real application, with only 20 seconds of simulation, they only study the transitory state. But, you can see that it is possible to use statistical models.)

If you are asking if it has sense for a practical application, No.

Why is not practical for real solutions?

The proposal needs some parameters that aren’t easy to measure in a real network, like the offered traffic, this value can change quickly and you need to communicate this value to all nodes, in a real network, when you have finish to communicate the value to all nodes, probably the value has changed, and it is more, the routing decision changes the aggregated lamda in the nodes, in summary, it is impractical in real applications.

Thanks for your all commitments sir!

To well understand the queuing mechanisms, I will refer you to study M/M/1 and M/G/1 type queuing schemes. This will also help you to develop some mathematical models for the said problem.

If you are working with multiple nodes then M/M/1 or M/D/1 models will not work, since these are 'tandem queues'. You will have look at more complex queuing models.

Muhammad Waqar i did too but still confused with. Have you tried similar scenario by your self before?

Shubham Gupta yeha am working on multiple nodes and that is why am getting confused with it. Thanks for all!

Bekan Kitaw Please check this article regarding the M/M/1 related concepts and implementation scenarios.

"Fronthaul Network Modeling and Dimensioning Meeting Ultra-low Latency Requirements for 5G" by Gabriel Otero Perez et al.

Muhammad Waqar tnx sir, but i got tired trying a lot. It seems difficult to integrate to what i'm looking for. did u tried working on those mechanism?

You can see this https://www.researchgate.net/post/How_can_I_model_an_M_G_1_queue_in_NetSim